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                <h1 id="LCT"><a href="#LCT" class="headerlink" title="LCT"></a>LCT</h1><h2 id="模板"><a href="#模板" class="headerlink" title="模板"></a>模板</h2><p><img src="https://img-blog.csdnimg.cn/633fff10368847c29a3847bd5f01e239.png" alt="在这里插入图片描述"></p>
<figure class="highlight cpp"><table><tbody><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string">&lt;bits/stdc++.h&gt;</span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N=<span class="number">1e5</span>+<span class="number">10</span>;</span><br><span class="line"></span><br><span class="line"><span class="keyword">struct</span> <span class="title class_">node</span>{</span><br><span class="line">    <span class="type">int</span> s[<span class="number">2</span>],p,v;</span><br><span class="line">    <span class="type">int</span> sum,rev;</span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> ls tr[u].s[0]</span></span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> lx tr[x].s[0]</span></span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> rs tr[u].s[1]</span></span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> rx tr[x].s[1]</span></span><br><span class="line">}tr[N];</span><br><span class="line"><span class="type">int</span> n,m,op,x,y;</span><br><span class="line"><span class="function"><span class="type">bool</span> <span class="keyword">inline</span> <span class="title">isroot</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    <span class="keyword">return</span> tr[tr[u].p].s[<span class="number">0</span>]!=u&amp;&amp;tr[tr[u].p].s[<span class="number">1</span>]!=u;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">pushup</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    tr[u].sum=tr[ls].sum^tr[u].v^tr[rs].sum;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">pushrev</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    <span class="built_in">swap</span>(ls,rs);</span><br><span class="line">    tr[u].rev^=<span class="number">1</span>;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">pushdown</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(tr[u].rev){</span><br><span class="line">        <span class="built_in">pushrev</span>(ls),<span class="built_in">pushrev</span>(rs);</span><br><span class="line">        tr[u].rev=<span class="number">0</span>;</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">rotate</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="type">int</span> y=tr[x].p,z=tr[y].p;</span><br><span class="line">    <span class="type">int</span> k=tr[y].s[<span class="number">1</span>]==x;</span><br><span class="line">    <span class="keyword">if</span>(!<span class="built_in">isroot</span>(y))tr[z].s[tr[z].s[<span class="number">1</span>]==y]=x;</span><br><span class="line">    tr[x].p=z;</span><br><span class="line">    tr[y].s[k]=tr[x].s[k^<span class="number">1</span>],tr[tr[x].s[k^<span class="number">1</span>]].p=y;</span><br><span class="line">    tr[x].s[k^<span class="number">1</span>]=y,tr[y].p=x;</span><br><span class="line">    <span class="built_in">pushup</span>(y),<span class="built_in">pushup</span>(x);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">splay</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="type">static</span> <span class="type">int</span> stk[N];</span><br><span class="line">    <span class="type">int</span> tt=<span class="number">0</span>,t=x;</span><br><span class="line">    stk[++tt]=t;</span><br><span class="line">    <span class="keyword">while</span>(!<span class="built_in">isroot</span>(t))stk[++tt]=t=tr[t].p;</span><br><span class="line">    <span class="keyword">while</span>(tt)<span class="built_in">pushdown</span>(stk[tt--]);</span><br><span class="line">    <span class="keyword">while</span>(!<span class="built_in">isroot</span>(x)){</span><br><span class="line">        <span class="type">int</span> y=tr[x].p,z=tr[y].p;</span><br><span class="line">        <span class="keyword">if</span>(!<span class="built_in">isroot</span>(y)){</span><br><span class="line">            <span class="keyword">if</span>( (tr[z].s[<span class="number">1</span>]==y)^(tr[y].s[<span class="number">1</span>]==x) )<span class="built_in">rotate</span>(x);</span><br><span class="line">            <span class="keyword">else</span> <span class="built_in">rotate</span>(y);</span><br><span class="line">        }<span class="built_in">rotate</span>(x);</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">access</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="type">int</span> z=x;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> y=<span class="number">0</span>;x;y=x,x=tr[x].p){</span><br><span class="line">        <span class="built_in">splay</span>(x);</span><br><span class="line">        rx=y;</span><br><span class="line">        <span class="built_in">pushup</span>(x);</span><br><span class="line">    }</span><br><span class="line">    <span class="built_in">splay</span>(z);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">makeroot</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="built_in">access</span>(x);</span><br><span class="line">    <span class="built_in">pushrev</span>(x);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="keyword">inline</span> <span class="title">findroot</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    <span class="built_in">access</span>(u);</span><br><span class="line">    <span class="keyword">while</span>(ls)<span class="built_in">pushdown</span>(u),u=ls;</span><br><span class="line">    <span class="built_in">splay</span>(u);</span><br><span class="line">    <span class="keyword">return</span> u;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">split</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="built_in">makeroot</span>(x);</span><br><span class="line">    <span class="built_in">access</span>(y);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">link</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="built_in">makeroot</span>(x);</span><br><span class="line">    <span class="keyword">if</span>(<span class="built_in">findroot</span>(y)!=x)tr[x].p=y;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">cut</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="built_in">makeroot</span>(x);</span><br><span class="line">    <span class="keyword">if</span>(<span class="built_in">findroot</span>(y)==x&amp;&amp;rx==y&amp;&amp;!tr[y].s[<span class="number">0</span>]){</span><br><span class="line">        tr[y].p=rx=<span class="number">0</span>;</span><br><span class="line">        <span class="built_in">pushup</span>(x);</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">signed</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line">    ios::<span class="built_in">sync_with_stdio</span>(<span class="number">0</span>);</span><br><span class="line">    cin.<span class="built_in">tie</span>(<span class="number">0</span>);</span><br><span class="line">    cout.<span class="built_in">tie</span>(<span class="number">0</span>);</span><br><span class="line">    cin&gt;&gt;n&gt;&gt;m;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n;i++)cin&gt;&gt;tr[i].v;</span><br><span class="line">    <span class="keyword">while</span>(m--){</span><br><span class="line">        cin&gt;&gt;op&gt;&gt;x&gt;&gt;y;</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="number">0</span>){</span><br><span class="line">            <span class="built_in">split</span>(x,y);</span><br><span class="line">            cout&lt;&lt;tr[y].sum&lt;&lt;<span class="string">'\n'</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="number">1</span>)<span class="built_in">link</span>(x,y);</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="number">2</span>)<span class="built_in">cut</span>(x,y);</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="number">3</span>){</span><br><span class="line">            <span class="built_in">splay</span>(x);</span><br><span class="line">            tr[x].v=y;</span><br><span class="line">            <span class="built_in">pushup</span>(x);</span><br><span class="line">        }</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table></figure>

<hr>
<h2 id="化边权为点权-动态维护区间最大值编号-用编号删边"><a href="#化边权为点权-动态维护区间最大值编号-用编号删边" class="headerlink" title="化边权为点权+动态维护区间最大值编号+用编号删边"></a>化边权为点权+动态维护区间最大值编号+用编号删边</h2><p><img src="https://img-blog.csdnimg.cn/119efad83ba64cdb8d2b017671a58db9.png" alt="在这里插入图片描述"></p>
<figure class="highlight cpp"><table><tbody><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span 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class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br><span class="line">114</span><br><span class="line">115</span><br><span class="line">116</span><br><span class="line">117</span><br><span class="line">118</span><br><span class="line">119</span><br><span class="line">120</span><br><span class="line">121</span><br><span class="line">122</span><br><span class="line">123</span><br><span class="line">124</span><br><span class="line">125</span><br><span class="line">126</span><br><span class="line">127</span><br><span class="line">128</span><br><span class="line">129</span><br><span class="line">130</span><br><span class="line">131</span><br><span class="line">132</span><br><span class="line">133</span><br><span class="line">134</span><br><span class="line">135</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string">&lt;bits/stdc++.h&gt;</span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N=<span class="number">1e6</span>+<span class="number">10</span>;</span><br><span class="line"><span class="type">int</span> n,m,p[N],stk[N];</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">find</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(p[x]!=x)p[x]=<span class="built_in">find</span>(p[x]);</span><br><span class="line">    <span class="keyword">return</span> p[x];</span><br><span class="line">}</span><br><span class="line"><span class="keyword">struct</span> <span class="title class_">Edge</span>{</span><br><span class="line">    <span class="type">int</span> x,y,a,b;</span><br><span class="line">    <span class="type">bool</span> <span class="keyword">operator</span>&lt;(<span class="type">const</span> Edge&amp;t)<span class="type">const</span>{</span><br><span class="line">        <span class="keyword">return</span> a&lt;t.a;</span><br><span class="line">    }</span><br><span class="line">}e[N];</span><br><span class="line"><span class="keyword">struct</span> <span class="title class_">node</span>{</span><br><span class="line">    <span class="type">int</span> s[<span class="number">2</span>],p,v;</span><br><span class="line">    <span class="type">int</span> mx,rev;</span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> ls tr[u].s[0]</span></span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> rs tr[u].s[1]</span></span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> lx tr[x].s[0]</span></span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> rx tr[x].s[1]</span></span><br><span class="line">}tr[N];</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">pushrev</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    <span class="built_in">swap</span>(ls,rs);</span><br><span class="line">    tr[u].rev^=<span class="number">1</span>;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">pushup</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    tr[u].mx=u;</span><br><span class="line">    <span class="type">int</span> lmaxid=tr[ls].mx;</span><br><span class="line">    <span class="type">int</span> rmaxid=tr[rs].mx;</span><br><span class="line">    <span class="keyword">if</span>(tr[lmaxid].v&gt;tr[tr[u].mx].v)tr[u].mx=lmaxid;</span><br><span class="line">    <span class="keyword">if</span>(tr[rmaxid].v&gt;tr[tr[u].mx].v)tr[u].mx=rmaxid;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">pushdown</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(tr[u].rev){</span><br><span class="line">        <span class="built_in">pushrev</span>(ls);</span><br><span class="line">        <span class="built_in">pushrev</span>(rs);</span><br><span class="line">        tr[u].rev=<span class="number">0</span>;</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">bool</span> <span class="title">isroot</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    <span class="keyword">return</span> tr[tr[u].p].s[<span class="number">0</span>]!=u&amp;&amp;tr[tr[u].p].s[<span class="number">1</span>]!=u;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">rotate</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="type">int</span> y=tr[x].p,z=tr[y].p;</span><br><span class="line">    <span class="type">int</span> k=tr[y].s[<span class="number">1</span>]==x;</span><br><span class="line">    <span class="keyword">if</span>(!<span class="built_in">isroot</span>(y))tr[z].s[tr[z].s[<span class="number">1</span>]==y]=x;</span><br><span class="line">    tr[x].p=z;</span><br><span class="line">    tr[y].s[k]=tr[x].s[k^<span class="number">1</span>],tr[tr[x].s[k^<span class="number">1</span>]].p=y;</span><br><span class="line">    tr[x].s[k^<span class="number">1</span>]=y,tr[y].p=x;</span><br><span class="line">    <span class="built_in">pushup</span>(y),<span class="built_in">pushup</span>(x);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">splay</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="type">int</span> top=<span class="number">0</span>,r=x;</span><br><span class="line">    stk[++top]=r;</span><br><span class="line">    <span class="keyword">while</span>(!<span class="built_in">isroot</span>(r))stk[++top]=r=tr[r].p;</span><br><span class="line">    <span class="keyword">while</span>(top)<span class="built_in">pushdown</span>(stk[top--]);</span><br><span class="line">    <span class="keyword">while</span>(!<span class="built_in">isroot</span>(x)){</span><br><span class="line">        <span class="type">int</span> y=tr[x].p,z=tr[y].p;</span><br><span class="line">        <span class="keyword">if</span>(!<span class="built_in">isroot</span>(y)){</span><br><span class="line">            <span class="keyword">if</span>((tr[z].s[<span class="number">1</span>]==y)^(tr[y].s[<span class="number">1</span>]==x))<span class="built_in">rotate</span>(x);</span><br><span class="line">            <span class="keyword">else</span> <span class="built_in">rotate</span>(y);</span><br><span class="line">        }</span><br><span class="line">        <span class="built_in">rotate</span>(x);</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">access</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="type">int</span> z=x;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> y=<span class="number">0</span>;x;y=x,x=tr[y].p){</span><br><span class="line">        <span class="built_in">splay</span>(x);</span><br><span class="line">        tr[x].s[<span class="number">1</span>]=y,<span class="built_in">pushup</span>(x);</span><br><span class="line">    }</span><br><span class="line">    <span class="built_in">splay</span>(z);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">makeroot</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="built_in">access</span>(x);</span><br><span class="line">    <span class="built_in">pushrev</span>(x);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">findroot</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="built_in">access</span>(x);</span><br><span class="line">    <span class="keyword">while</span>(lx)<span class="built_in">pushdown</span>(x),x=lx;</span><br><span class="line">    <span class="built_in">splay</span>(x);</span><br><span class="line">    <span class="keyword">return</span> x;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">split</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="built_in">makeroot</span>(x);</span><br><span class="line">    <span class="built_in">access</span>(y);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">link</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="built_in">makeroot</span>(x);</span><br><span class="line">    <span class="keyword">if</span>(<span class="built_in">findroot</span>(y)!=x)tr[x].p=y;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">cut</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="built_in">makeroot</span>(x);</span><br><span class="line">    <span class="keyword">if</span>(<span class="built_in">findroot</span>(y)==x&amp;&amp;rx==y&amp;&amp;!tr[y].s[<span class="number">0</span>]){</span><br><span class="line">        tr[y].p=rx=<span class="number">0</span>;</span><br><span class="line">        <span class="built_in">pushup</span>(x);</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">signed</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line">    ios::<span class="built_in">sync_with_stdio</span>(<span class="number">0</span>);cin.<span class="built_in">tie</span>(<span class="number">0</span>);cout.<span class="built_in">tie</span>(<span class="number">0</span>);</span><br><span class="line">    cin&gt;&gt;n&gt;&gt;m;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=m;i++){</span><br><span class="line">        <span class="type">int</span> x,y,a,b;</span><br><span class="line">        cin&gt;&gt;x&gt;&gt;y&gt;&gt;a&gt;&gt;b;</span><br><span class="line">        e[i]={x,y,a,b};</span><br><span class="line">    }</span><br><span class="line">    <span class="built_in">sort</span>(e+<span class="number">1</span>,e+<span class="number">1</span>+m);</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n+m;i++){</span><br><span class="line">        p[i]=i;</span><br><span class="line">        <span class="keyword">if</span>(i&gt;n)tr[i].v=e[i-n].b;</span><br><span class="line">        tr[i].mx=i;</span><br><span class="line">    }</span><br><span class="line">    <span class="type">int</span> ans=<span class="number">1e9</span>;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=m;i++){</span><br><span class="line">        <span class="type">int</span> x=e[i].x,y=e[i].y,a=e[i].a,b=e[i].b;</span><br><span class="line">        <span class="keyword">if</span>(<span class="built_in">find</span>(x)==<span class="built_in">find</span>(y)){</span><br><span class="line">            <span class="built_in">split</span>(x,y);</span><br><span class="line">            <span class="type">int</span> t=tr[y].mx;</span><br><span class="line">            <span class="keyword">if</span>(tr[t].v&gt;b){</span><br><span class="line">                <span class="built_in">cut</span>(t,e[t-n].x),<span class="built_in">cut</span>(t,e[t-n].y);</span><br><span class="line">                <span class="built_in">link</span>(i+n,x),<span class="built_in">link</span>(i+n,y);</span><br><span class="line">            }</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span>{</span><br><span class="line">            p[<span class="built_in">find</span>(x)]=<span class="built_in">find</span>(y);</span><br><span class="line">            <span class="built_in">link</span>(i+n,x),<span class="built_in">link</span>(i+n,y);</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">if</span>(<span class="built_in">find</span>(<span class="number">1</span>)==<span class="built_in">find</span>(n)){</span><br><span class="line">            <span class="built_in">split</span>(<span class="number">1</span>,n);</span><br><span class="line">            ans=<span class="built_in">min</span>(ans,a+tr[tr[n].mx].v);</span><br><span class="line">        }</span><br><span class="line">    }</span><br><span class="line">    cout&lt;&lt;(ans==<span class="number">1e9</span>?<span class="number">-1</span>:ans);</span><br><span class="line">}</span><br></pre></td></tr></tbody></table></figure>



<h2 id="lct求子树大小"><a href="#lct求子树大小" class="headerlink" title="lct求子树大小"></a>lct求子树大小</h2><p><img src="https://img-blog.csdnimg.cn/3d3130ffc83d4809acd5691ead77baaa.png" alt="在这里插入图片描述"></p>
<figure class="highlight cpp"><table><tbody><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span 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class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br><span class="line">114</span><br><span class="line">115</span><br><span class="line">116</span><br><span class="line">117</span><br><span class="line">118</span><br><span class="line">119</span><br><span class="line">120</span><br><span class="line">121</span><br><span class="line">122</span><br><span class="line">123</span><br><span class="line">124</span><br><span class="line">125</span><br><span class="line">126</span><br><span class="line">127</span><br><span class="line">128</span><br><span class="line">129</span><br><span class="line">130</span><br><span class="line">131</span><br><span class="line">132</span><br><span class="line">133</span><br><span class="line">134</span><br><span class="line">135</span><br><span class="line">136</span><br><span class="line">137</span><br><span class="line">138</span><br><span class="line">139</span><br><span class="line">140</span><br><span class="line">141</span><br><span class="line">142</span><br><span class="line">143</span><br><span class="line">144</span><br><span class="line">145</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string">&lt;cstdio&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string">&lt;cstdlib&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string">&lt;cstring&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string">&lt;cmath&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string">&lt;iostream&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string">&lt;iomanip&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string">&lt;algorithm&gt;</span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"><span class="keyword">struct</span> <span class="title class_">node</span>{</span><br><span class="line">	<span class="type">int</span> fa,son[<span class="number">2</span>],siz,exsiz,rev;</span><br><span class="line">}t[<span class="number">100050</span>];</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">update</span><span class="params">(<span class="type">int</span> x)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line">	t[x].siz=t[t[x].son[<span class="number">0</span>]].siz+t[t[x].son[<span class="number">1</span>]].siz+t[x].exsiz+<span class="number">1</span>;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">pushdown</span><span class="params">(<span class="type">int</span> x)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line">	<span class="keyword">if</span>(t[x].rev)</span><br><span class="line">	{</span><br><span class="line">		<span class="built_in">swap</span>(t[x].son[<span class="number">0</span>],t[x].son[<span class="number">1</span>]);</span><br><span class="line">		<span class="keyword">if</span>(t[x].son[<span class="number">0</span>]) t[t[x].son[<span class="number">0</span>]].rev^=<span class="number">1</span>;</span><br><span class="line">		<span class="keyword">if</span>(t[x].son[<span class="number">1</span>]) t[t[x].son[<span class="number">1</span>]].rev^=<span class="number">1</span>;</span><br><span class="line">		t[x].rev=<span class="number">0</span>;</span><br><span class="line">	}</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="type">bool</span> <span class="title">isroot</span><span class="params">(<span class="type">int</span> x)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line">	<span class="keyword">return</span> t[t[x].fa].son[<span class="number">0</span>]!=x&amp;&amp;t[t[x].fa].son[<span class="number">1</span>]!=x;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="type">int</span> <span class="title">get</span><span class="params">(<span class="type">int</span> x)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line">	<span class="keyword">return</span> t[t[x].fa].son[<span class="number">1</span>]==x;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">rotate</span><span class="params">(<span class="type">int</span> x)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line">	<span class="type">int</span> f=t[x].fa;<span class="type">int</span> ff=t[f].fa;<span class="type">int</span> gx=<span class="built_in">get</span>(x);<span class="type">int</span> gx2=<span class="built_in">get</span>(f);</span><br><span class="line">	<span class="keyword">if</span>(!<span class="built_in">isroot</span>(f))</span><br><span class="line">	{</span><br><span class="line">		t[ff].son[gx2]=x;</span><br><span class="line">	}</span><br><span class="line">	t[f].son[gx]=t[x].son[gx^<span class="number">1</span>];</span><br><span class="line">	t[t[x].son[gx^<span class="number">1</span>]].fa=f;</span><br><span class="line">	t[x].son[gx^<span class="number">1</span>]=f;</span><br><span class="line">	t[f].fa=x;</span><br><span class="line">	t[x].fa=ff;</span><br><span class="line">	<span class="built_in">update</span>(f);</span><br><span class="line">	<span class="built_in">update</span>(x);</span><br><span class="line">}</span><br><span class="line"><span class="type">int</span> st[<span class="number">100050</span>];</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">splay</span><span class="params">(<span class="type">int</span> x)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line">	<span class="type">int</span> top=<span class="number">0</span>;</span><br><span class="line">	<span class="type">int</span> y=x;</span><br><span class="line">	st[++top]=y;</span><br><span class="line">	<span class="keyword">while</span>(!<span class="built_in">isroot</span>(y))</span><br><span class="line">	{</span><br><span class="line">		y=t[y].fa;</span><br><span class="line">		st[++top]=y;</span><br><span class="line">	}</span><br><span class="line">	<span class="keyword">while</span>(top)</span><br><span class="line">	{</span><br><span class="line">		<span class="built_in">pushdown</span>(st[top--]);</span><br><span class="line">	}</span><br><span class="line">	<span class="keyword">while</span>(!<span class="built_in">isroot</span>(x))</span><br><span class="line">	{</span><br><span class="line">		<span class="type">int</span> f=t[x].fa;</span><br><span class="line">		<span class="keyword">if</span>(<span class="built_in">isroot</span>(f))</span><br><span class="line">		{</span><br><span class="line">			<span class="built_in">rotate</span>(x);</span><br><span class="line">		}</span><br><span class="line">		<span class="keyword">else</span> <span class="keyword">if</span>(<span class="built_in">get</span>(x)==<span class="built_in">get</span>(f))</span><br><span class="line">		{</span><br><span class="line">			<span class="built_in">rotate</span>(f);</span><br><span class="line">			<span class="built_in">rotate</span>(x);</span><br><span class="line">		}</span><br><span class="line">		<span class="keyword">else</span> </span><br><span class="line">		{</span><br><span class="line">			<span class="built_in">rotate</span>(x);</span><br><span class="line">			<span class="built_in">rotate</span>(x);</span><br><span class="line">		}</span><br><span class="line">		<span class="built_in">update</span>(x);</span><br><span class="line">	}</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">access</span><span class="params">(<span class="type">int</span> x)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line">	<span class="keyword">for</span>(<span class="type">int</span> y=<span class="number">0</span>;x;y=x,x=t[x].fa)</span><br><span class="line">	{</span><br><span class="line">		<span class="built_in">splay</span>(x);</span><br><span class="line">		t[x].exsiz+=t[t[x].son[<span class="number">1</span>]].siz-t[y].siz;</span><br><span class="line">		t[x].son[<span class="number">1</span>]=y;</span><br><span class="line">		<span class="built_in">update</span>(x);</span><br><span class="line">	}</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">makeroot</span><span class="params">(<span class="type">int</span> x)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line">	<span class="built_in">access</span>(x);</span><br><span class="line">	<span class="built_in">splay</span>(x);</span><br><span class="line">	t[x].rev^=<span class="number">1</span>;</span><br><span class="line">	<span class="built_in">pushdown</span>(x);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">link</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line">	<span class="built_in">makeroot</span>(x);</span><br><span class="line">	<span class="built_in">makeroot</span>(y);</span><br><span class="line">	t[x].fa=y;</span><br><span class="line">	t[y].exsiz+=t[x].siz;</span><br><span class="line">	<span class="built_in">update</span>(y);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">split</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line">	<span class="built_in">makeroot</span>(x);</span><br><span class="line">	<span class="built_in">access</span>(y);</span><br><span class="line">	<span class="built_in">splay</span>(y);</span><br><span class="line">}</span><br><span class="line"><span class="type">int</span> n,q;</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line">	 <span class="built_in">scanf</span>(<span class="string">"%d%d"</span>,&amp;n,&amp;q);</span><br><span class="line">	 <span class="keyword">while</span>(q--)</span><br><span class="line">	 {</span><br><span class="line">	 	<span class="type">char</span> typ;</span><br><span class="line">	 	cin&gt;&gt;typ;</span><br><span class="line">	 	<span class="keyword">if</span>(typ==<span class="string">'A'</span>)</span><br><span class="line">	 	{</span><br><span class="line">	 		<span class="type">int</span> x,y;</span><br><span class="line">	 		<span class="built_in">scanf</span>(<span class="string">"%d%d"</span>,&amp;x,&amp;y);</span><br><span class="line">	 		<span class="built_in">link</span>(x,y);</span><br><span class="line">		}</span><br><span class="line">		<span class="keyword">else</span></span><br><span class="line">		{</span><br><span class="line">			<span class="type">int</span> x,y;</span><br><span class="line">			<span class="built_in">scanf</span>(<span class="string">"%d%d"</span>,&amp;x,&amp;y);</span><br><span class="line">			<span class="built_in">split</span>(x,y);</span><br><span class="line">			t[y].son[<span class="number">0</span>]=t[x].fa=<span class="number">0</span>;</span><br><span class="line">			<span class="built_in">update</span>(y);</span><br><span class="line">			<span class="built_in">makeroot</span>(x);</span><br><span class="line">			<span class="built_in">makeroot</span>(y);</span><br><span class="line">			<span class="type">long</span> <span class="type">long</span> ans=(<span class="type">long</span> <span class="type">long</span>)(t[x].siz)*(<span class="type">long</span> <span class="type">long</span>)(t[y].siz);</span><br><span class="line">			<span class="built_in">printf</span>(<span class="string">"%lld\n"</span>,ans);</span><br><span class="line">			t[x].fa=y;</span><br><span class="line">			t[y].exsiz+=t[x].siz;</span><br><span class="line">		}</span><br><span class="line">	 }</span><br><span class="line">	 <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line"> } </span><br></pre></td></tr></tbody></table></figure>

<hr>
<h2 id="弹飞绵羊"><a href="#弹飞绵羊" class="headerlink" title="弹飞绵羊"></a>弹飞绵羊</h2><figure class="highlight cpp"><table><tbody><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br><span class="line">114</span><br><span class="line">115</span><br><span class="line">116</span><br><span class="line">117</span><br><span class="line">118</span><br><span class="line">119</span><br><span class="line">120</span><br><span class="line">121</span><br><span class="line">122</span><br><span class="line">123</span><br><span class="line">124</span><br><span class="line">125</span><br><span class="line">126</span><br><span class="line">127</span><br><span class="line">128</span><br><span class="line">129</span><br><span class="line">130</span><br><span class="line">131</span><br><span class="line">132</span><br><span class="line">133</span><br><span class="line">134</span><br><span class="line">135</span><br><span class="line">136</span><br><span class="line">137</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string">&lt;bits/stdc++.h&gt;</span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N=<span class="number">1e6</span>+<span class="number">10</span>;</span><br><span class="line"></span><br><span class="line"><span class="keyword">struct</span> <span class="title class_">node</span>{</span><br><span class="line">    <span class="type">int</span> s[<span class="number">2</span>],p,v;</span><br><span class="line">    <span class="type">int</span> sum,rev;</span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> ls tr[u].s[0]</span></span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> lx tr[x].s[0]</span></span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> rs tr[u].s[1]</span></span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> rx tr[x].s[1]</span></span><br><span class="line">}tr[N];</span><br><span class="line"><span class="type">int</span> n,m,op,x,y;</span><br><span class="line"><span class="function"><span class="type">bool</span> <span class="keyword">inline</span> <span class="title">isroot</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    <span class="keyword">return</span> tr[tr[u].p].s[<span class="number">0</span>]!=u&amp;&amp;tr[tr[u].p].s[<span class="number">1</span>]!=u;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">pushup</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    tr[u].sum=tr[ls].sum+tr[u].v+tr[rs].sum;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">pushrev</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    <span class="built_in">swap</span>(ls,rs);</span><br><span class="line">    tr[u].rev^=<span class="number">1</span>;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">pushdown</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(tr[u].rev){</span><br><span class="line">        <span class="built_in">pushrev</span>(ls),<span class="built_in">pushrev</span>(rs);</span><br><span class="line">        tr[u].rev=<span class="number">0</span>;</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">rotate</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="type">int</span> y=tr[x].p,z=tr[y].p;</span><br><span class="line">    <span class="type">int</span> k=tr[y].s[<span class="number">1</span>]==x;</span><br><span class="line">    <span class="keyword">if</span>(!<span class="built_in">isroot</span>(y))tr[z].s[tr[z].s[<span class="number">1</span>]==y]=x;</span><br><span class="line">    tr[x].p=z;</span><br><span class="line">    tr[y].s[k]=tr[x].s[k^<span class="number">1</span>],tr[tr[x].s[k^<span class="number">1</span>]].p=y;</span><br><span class="line">    tr[x].s[k^<span class="number">1</span>]=y,tr[y].p=x;</span><br><span class="line">    <span class="built_in">pushup</span>(y),<span class="built_in">pushup</span>(x);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">splay</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="type">static</span> <span class="type">int</span> stk[N];</span><br><span class="line">    <span class="type">int</span> tt=<span class="number">0</span>,t=x;</span><br><span class="line">    stk[++tt]=t;</span><br><span class="line">    <span class="keyword">while</span>(!<span class="built_in">isroot</span>(t))stk[++tt]=t=tr[t].p;</span><br><span class="line">    <span class="keyword">while</span>(tt)<span class="built_in">pushdown</span>(stk[tt--]);</span><br><span class="line">    <span class="keyword">while</span>(!<span class="built_in">isroot</span>(x)){</span><br><span class="line">        <span class="type">int</span> y=tr[x].p,z=tr[y].p;</span><br><span class="line">        <span class="keyword">if</span>(!<span class="built_in">isroot</span>(y)){</span><br><span class="line">            <span class="keyword">if</span>( (tr[z].s[<span class="number">1</span>]==y)^(tr[y].s[<span class="number">1</span>]==x) )<span class="built_in">rotate</span>(x);</span><br><span class="line">            <span class="keyword">else</span> <span class="built_in">rotate</span>(y);</span><br><span class="line">        }<span class="built_in">rotate</span>(x);</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">access</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="type">int</span> z=x;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> y=<span class="number">0</span>;x;y=x,x=tr[x].p){</span><br><span class="line">        <span class="built_in">splay</span>(x);</span><br><span class="line">        rx=y;</span><br><span class="line">        <span class="built_in">pushup</span>(x);</span><br><span class="line">    }</span><br><span class="line">    <span class="built_in">splay</span>(z);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">makeroot</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="built_in">access</span>(x);</span><br><span class="line">    <span class="built_in">pushrev</span>(x);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="keyword">inline</span> <span class="title">findroot</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    <span class="built_in">access</span>(u);</span><br><span class="line">    <span class="keyword">while</span>(ls)<span class="built_in">pushdown</span>(u),u=ls;</span><br><span class="line">    <span class="built_in">splay</span>(u);</span><br><span class="line">    <span class="keyword">return</span> u;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">split</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="built_in">makeroot</span>(x);</span><br><span class="line">    <span class="built_in">access</span>(y);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">link</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="built_in">makeroot</span>(x);</span><br><span class="line">    <span class="keyword">if</span>(<span class="built_in">findroot</span>(y)!=x)tr[x].p=y;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">cut</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="built_in">makeroot</span>(x);</span><br><span class="line">    <span class="keyword">if</span>(<span class="built_in">findroot</span>(y)==x&amp;&amp;rx==y&amp;&amp;!tr[y].s[<span class="number">0</span>]){</span><br><span class="line">        tr[y].p=rx=<span class="number">0</span>;</span><br><span class="line">        <span class="built_in">pushup</span>(x);</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="type">int</span> fa[N];</span><br><span class="line"><span class="function"><span class="type">signed</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line">    ios::<span class="built_in">sync_with_stdio</span>(<span class="number">0</span>);</span><br><span class="line">    cin.<span class="built_in">tie</span>(<span class="number">0</span>);</span><br><span class="line">    cout.<span class="built_in">tie</span>(<span class="number">0</span>);</span><br><span class="line">    <span class="comment">// cin&gt;&gt;n&gt;&gt;m;</span></span><br><span class="line">    <span class="comment">// for(int i=1;i&lt;=n;i++)cin&gt;&gt;tr[i].v;</span></span><br><span class="line">    <span class="comment">// while(m--){</span></span><br><span class="line">    <span class="comment">//     cin&gt;&gt;op&gt;&gt;x&gt;&gt;y;</span></span><br><span class="line">    <span class="comment">//     if(op==0){</span></span><br><span class="line">    <span class="comment">//         split(x,y);</span></span><br><span class="line">    <span class="comment">//         cout&lt;&lt;tr[y].sum&lt;&lt;'\n';</span></span><br><span class="line">    <span class="comment">//     }</span></span><br><span class="line">    <span class="comment">//     if(op==1)link(x,y);</span></span><br><span class="line">    <span class="comment">//     if(op==2)cut(x,y);</span></span><br><span class="line">    <span class="comment">//     if(op==3){</span></span><br><span class="line">    <span class="comment">//         splay(x);</span></span><br><span class="line">    <span class="comment">//         tr[x].v=y;</span></span><br><span class="line">    <span class="comment">//         pushup(x);</span></span><br><span class="line">    <span class="comment">//     }</span></span><br><span class="line">    <span class="comment">// }</span></span><br><span class="line">    cin&gt;&gt;n;</span><br><span class="line">    <span class="type">int</span> T=n+<span class="number">1</span>;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n+<span class="number">1</span>;i++)tr[i].v=<span class="number">1</span>;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n;i++){</span><br><span class="line">        cin&gt;&gt;fa[i];</span><br><span class="line">        fa[i]=<span class="built_in">min</span>(fa[i]+i,n+<span class="number">1</span>);</span><br><span class="line">        <span class="built_in">link</span>(i,fa[i]);</span><br><span class="line">    }</span><br><span class="line">    cin&gt;&gt;m;</span><br><span class="line">    <span class="keyword">while</span>(m--){</span><br><span class="line">        <span class="type">int</span> op;</span><br><span class="line">        cin&gt;&gt;op;</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="number">1</span>){</span><br><span class="line">            <span class="type">int</span> x;</span><br><span class="line">            cin&gt;&gt;x;</span><br><span class="line">            x++;</span><br><span class="line">            <span class="built_in">split</span>(x,T);</span><br><span class="line">            cout&lt;&lt;tr[T].sum<span class="number">-1</span>&lt;&lt;<span class="string">'\n'</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">else</span>{</span><br><span class="line">            <span class="type">int</span> x,f;</span><br><span class="line">            cin&gt;&gt;x&gt;&gt;f;</span><br><span class="line">            x++;</span><br><span class="line">            <span class="built_in">cut</span>(x,fa[x]);</span><br><span class="line">            f=<span class="built_in">min</span>(T,f+x);</span><br><span class="line">            fa[x]=f;</span><br><span class="line">            <span class="built_in">link</span>(x,f);</span><br><span class="line">        }</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table></figure>

<hr>
<h2 id="树上求割边割点数量"><a href="#树上求割边割点数量" class="headerlink" title="树上求割边割点数量"></a>树上求割边割点数量</h2><p><img src="https://img-blog.csdnimg.cn/0b6e167bccd14aa2b23adb62eb51fce1.png" alt="在这里插入图片描述"></p>
<figure class="highlight cpp"><table><tbody><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br><span class="line">114</span><br><span class="line">115</span><br><span class="line">116</span><br><span class="line">117</span><br><span class="line">118</span><br><span class="line">119</span><br><span class="line">120</span><br><span class="line">121</span><br><span class="line">122</span><br><span class="line">123</span><br><span class="line">124</span><br><span class="line">125</span><br><span class="line">126</span><br><span class="line">127</span><br><span class="line">128</span><br><span class="line">129</span><br><span class="line">130</span><br><span class="line">131</span><br><span class="line">132</span><br><span class="line">133</span><br><span class="line">134</span><br><span class="line">135</span><br><span class="line">136</span><br><span class="line">137</span><br><span class="line">138</span><br><span class="line">139</span><br><span class="line">140</span><br><span class="line">141</span><br><span class="line">142</span><br><span class="line">143</span><br><span class="line">144</span><br><span class="line">145</span><br><span class="line">146</span><br><span class="line">147</span><br><span class="line">148</span><br><span class="line">149</span><br><span class="line">150</span><br><span class="line">151</span><br><span class="line">152</span><br><span class="line">153</span><br><span class="line">154</span><br><span class="line">155</span><br><span class="line">156</span><br><span class="line">157</span><br><span class="line">158</span><br><span class="line">159</span><br><span class="line">160</span><br><span class="line">161</span><br><span class="line">162</span><br><span class="line">163</span><br><span class="line">164</span><br><span class="line">165</span><br><span class="line">166</span><br><span class="line">167</span><br><span class="line">168</span><br><span class="line">169</span><br><span class="line">170</span><br><span class="line">171</span><br><span class="line">172</span><br><span class="line">173</span><br><span class="line">174</span><br><span class="line">175</span><br><span class="line">176</span><br><span class="line">177</span><br><span class="line">178</span><br><span class="line">179</span><br><span class="line">180</span><br><span class="line">181</span><br><span class="line">182</span><br><span class="line">183</span><br><span class="line">184</span><br><span class="line">185</span><br><span class="line">186</span><br><span class="line">187</span><br><span class="line">188</span><br><span class="line">189</span><br><span class="line">190</span><br><span class="line">191</span><br><span class="line">192</span><br><span class="line">193</span><br><span class="line">194</span><br><span class="line">195</span><br><span class="line">196</span><br><span class="line">197</span><br><span class="line">198</span><br><span class="line">199</span><br><span class="line">200</span><br><span class="line">201</span><br><span class="line">202</span><br><span class="line">203</span><br><span class="line">204</span><br><span class="line">205</span><br><span class="line">206</span><br><span class="line">207</span><br><span class="line">208</span><br><span class="line">209</span><br><span class="line">210</span><br><span class="line">211</span><br><span class="line">212</span><br><span class="line">213</span><br><span class="line">214</span><br><span class="line">215</span><br><span class="line">216</span><br><span class="line">217</span><br><span class="line">218</span><br><span class="line">219</span><br><span class="line">220</span><br><span class="line">221</span><br><span class="line">222</span><br><span class="line">223</span><br><span class="line">224</span><br><span class="line">225</span><br><span class="line">226</span><br><span class="line">227</span><br><span class="line">228</span><br><span class="line">229</span><br><span class="line">230</span><br><span class="line">231</span><br><span class="line">232</span><br><span class="line">233</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;cstdio&gt;</span></span></span><br><span class="line"></span><br><span class="line"><span class="meta">#<span class="keyword">define</span> N 200010</span></span><br><span class="line"><span class="meta">#<span class="keyword">define</span> lc(x) ch[x][0]</span></span><br><span class="line"><span class="meta">#<span class="keyword">define</span> rc(x) ch[x][1]</span></span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">swap</span><span class="params">(<span class="type">int</span>&amp;a,<span class="type">int</span>&amp;b)</span> </span>{</span><br><span class="line">	<span class="function"><span class="type">int</span> <span class="title">tmp</span><span class="params">(a)</span></span>; a=b,b=tmp;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="keyword">namespace</span> Summer {</span><br><span class="line">	<span class="type">int</span> ch[N][<span class="number">2</span>],fa[N],rev[N],val[N],sumv[N],mark[N];</span><br><span class="line">	<span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">reverse</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">		<span class="keyword">if</span>(x) {</span><br><span class="line">			<span class="built_in">swap</span>(<span class="built_in">lc</span>(x),<span class="built_in">rc</span>(x));</span><br><span class="line">			rev[x]^=<span class="number">1</span>;</span><br><span class="line">		}</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">NaCly_Fish_Orz</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">		<span class="keyword">if</span>(x) {</span><br><span class="line">			val[x]=sumv[x]=<span class="number">0</span>;</span><br><span class="line">			mark[x]=<span class="number">1</span>;</span><br><span class="line">		}</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">up</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">		sumv[x]=sumv[<span class="built_in">lc</span>(x)]+sumv[<span class="built_in">rc</span>(x)]+val[x];</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">down</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">		<span class="keyword">if</span>(rev[x]) {</span><br><span class="line">			<span class="built_in">reverse</span>(<span class="built_in">lc</span>(x));</span><br><span class="line">			<span class="built_in">reverse</span>(<span class="built_in">rc</span>(x));</span><br><span class="line">			rev[x]=<span class="number">0</span>;</span><br><span class="line">		}</span><br><span class="line">		<span class="keyword">if</span>(mark[x]) {</span><br><span class="line">			<span class="built_in">NaCly_Fish_Orz</span>(<span class="built_in">lc</span>(x));</span><br><span class="line">			<span class="built_in">NaCly_Fish_Orz</span>(<span class="built_in">rc</span>(x));</span><br><span class="line">			mark[x]=<span class="number">0</span>;</span><br><span class="line">		}</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="keyword">inline</span> <span class="type">int</span> <span class="title">nrt</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">		<span class="keyword">return</span> x==<span class="built_in">lc</span>(fa[x])||x==<span class="built_in">rc</span>(fa[x]);</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="type">void</span> <span class="title">psa</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">		<span class="keyword">if</span>(<span class="built_in">nrt</span>(x)) <span class="built_in">psa</span>(fa[x]);</span><br><span class="line">		<span class="built_in">down</span>(x);</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">rotate</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">		<span class="function"><span class="type">int</span> <span class="title">y</span><span class="params">(fa[x])</span>,<span class="title">z</span><span class="params">(fa[y])</span>,<span class="title">k</span><span class="params">(x==rc(y))</span></span>;</span><br><span class="line">		ch[y][k]=ch[x][k^<span class="number">1</span>],ch[x][k^<span class="number">1</span>]=y;</span><br><span class="line">		<span class="keyword">if</span>(<span class="built_in">nrt</span>(y)) ch[z][y==<span class="built_in">rc</span>(z)]=x;</span><br><span class="line">		<span class="keyword">if</span>(ch[y][k]) fa[ch[y][k]]=y;</span><br><span class="line">		fa[y]=x,fa[x]=z,<span class="built_in">up</span>(y);</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">splay</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">		<span class="type">int</span> y,z;</span><br><span class="line">		<span class="keyword">for</span>(<span class="built_in">psa</span>(x);<span class="built_in">nrt</span>(x);<span class="built_in">rotate</span>(x)) {</span><br><span class="line">			y=fa[x],z=fa[y];</span><br><span class="line">			<span class="keyword">if</span>(<span class="built_in">nrt</span>(y)) <span class="built_in">rotate</span>(x==<span class="built_in">rc</span>(y)^y==<span class="built_in">rc</span>(z)?x:y);</span><br><span class="line">		} <span class="built_in">up</span>(x);</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">access</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">		<span class="keyword">for</span>(<span class="type">int</span> y=<span class="number">0</span>;x;x=fa[y=x]) {</span><br><span class="line">			<span class="built_in">splay</span>(x); <span class="built_in">rc</span>(x)=y; <span class="built_in">up</span>(x);</span><br><span class="line">		}</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">mrt</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">		<span class="built_in">access</span>(x); <span class="built_in">splay</span>(x); <span class="built_in">reverse</span>(x);</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">link</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span> </span>{</span><br><span class="line">		<span class="built_in">mrt</span>(x); fa[x]=y;</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">cut</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span> </span>{</span><br><span class="line">		<span class="built_in">mrt</span>(x); <span class="built_in">access</span>(y); <span class="built_in">splay</span>(y);</span><br><span class="line">		fa[x]=<span class="built_in">lc</span>(y)=<span class="number">0</span>; <span class="built_in">up</span>(y);</span><br><span class="line">	}</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="keyword">namespace</span> Pockets {</span><br><span class="line">	<span class="type">int</span> ch[N][<span class="number">2</span>],fa[N],rev[N],val[N],sumv[N],st[N],num;</span><br><span class="line">	<span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">reverse</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">		<span class="keyword">if</span>(x) {</span><br><span class="line">			<span class="built_in">swap</span>(<span class="built_in">lc</span>(x),<span class="built_in">rc</span>(x));</span><br><span class="line">			rev[x]^=<span class="number">1</span>;</span><br><span class="line">		}</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">up</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">		sumv[x]=sumv[<span class="built_in">lc</span>(x)]+sumv[<span class="built_in">rc</span>(x)]+val[x];</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">down</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">		<span class="keyword">if</span>(rev[x]) {</span><br><span class="line">			<span class="built_in">reverse</span>(<span class="built_in">lc</span>(x));</span><br><span class="line">			<span class="built_in">reverse</span>(<span class="built_in">rc</span>(x));</span><br><span class="line">			rev[x]=<span class="number">0</span>;</span><br><span class="line">		}</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="keyword">inline</span> <span class="type">int</span> <span class="title">nrt</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">		<span class="keyword">return</span> x==<span class="built_in">lc</span>(fa[x])||x==<span class="built_in">rc</span>(fa[x]);</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="type">void</span> <span class="title">psa</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">		<span class="keyword">if</span>(<span class="built_in">nrt</span>(x)) <span class="built_in">psa</span>(fa[x]);</span><br><span class="line">		<span class="built_in">down</span>(x);</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">rotate</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">		<span class="function"><span class="type">int</span> <span class="title">y</span><span class="params">(fa[x])</span>,<span class="title">z</span><span class="params">(fa[y])</span>,<span class="title">k</span><span class="params">(x==rc(y))</span></span>;</span><br><span class="line">		ch[y][k]=ch[x][k^<span class="number">1</span>],ch[x][k^<span class="number">1</span>]=y;</span><br><span class="line">		<span class="keyword">if</span>(<span class="built_in">nrt</span>(y)) ch[z][y==<span class="built_in">rc</span>(z)]=x;</span><br><span class="line">		<span class="keyword">if</span>(ch[y][k]) fa[ch[y][k]]=y;</span><br><span class="line">		fa[y]=x,fa[x]=z,<span class="built_in">up</span>(y);</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">splay</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">		<span class="type">int</span> y,z;</span><br><span class="line">		<span class="keyword">for</span>(<span class="built_in">psa</span>(x);<span class="built_in">nrt</span>(x);<span class="built_in">rotate</span>(x)) {</span><br><span class="line">			y=fa[x],z=fa[y];</span><br><span class="line">			<span class="keyword">if</span>(<span class="built_in">nrt</span>(y)) <span class="built_in">rotate</span>(x==<span class="built_in">rc</span>(y)^y==<span class="built_in">rc</span>(z)?x:y);</span><br><span class="line">		} <span class="built_in">up</span>(x);</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">access</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">		<span class="keyword">for</span>(<span class="type">int</span> y=<span class="number">0</span>;x;x=fa[y=x]) {</span><br><span class="line">			<span class="built_in">splay</span>(x); <span class="built_in">rc</span>(x)=y; <span class="built_in">up</span>(x);</span><br><span class="line">		}</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">mrt</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">		<span class="built_in">access</span>(x); <span class="built_in">splay</span>(x); <span class="built_in">reverse</span>(x);</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">link</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span> </span>{</span><br><span class="line">		<span class="built_in">mrt</span>(x); fa[x]=y;</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">cut</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span> </span>{</span><br><span class="line">		<span class="built_in">mrt</span>(x); <span class="built_in">access</span>(y); <span class="built_in">splay</span>(y);</span><br><span class="line">		fa[x]=<span class="built_in">lc</span>(y)=<span class="number">0</span>; <span class="built_in">up</span>(y);</span><br><span class="line">	}</span><br><span class="line">	<span class="function"><span class="type">void</span> <span class="title">print</span><span class="params">(<span class="type">int</span> now)</span> </span>{</span><br><span class="line">		<span class="keyword">if</span>(now) {</span><br><span class="line">			<span class="built_in">down</span>(now);</span><br><span class="line">			<span class="built_in">print</span>(<span class="built_in">lc</span>(now));</span><br><span class="line">			st[++num]=now;</span><br><span class="line">			<span class="built_in">print</span>(<span class="built_in">rc</span>(now));</span><br><span class="line">		}</span><br><span class="line">	}</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> n,q,opt,u,v,last,tot,ans,SummerPockets;</span><br><span class="line"></span><br><span class="line"><span class="type">int</span> fa[N];</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="type">int</span> <span class="title">find</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">	<span class="keyword">return</span> x==fa[x]?x:fa[x]=<span class="built_in">find</span>(fa[x]);</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">getEdge</span><span class="params">(<span class="type">int</span> u,<span class="type">int</span> v)</span> </span>{</span><br><span class="line">	<span class="type">int</span> x=<span class="built_in">find</span>(u),y=<span class="built_in">find</span>(v);</span><br><span class="line">	<span class="keyword">if</span>(x!=y) {</span><br><span class="line">		ans=<span class="number">-1</span>;</span><br><span class="line">		<span class="keyword">return</span>;</span><br><span class="line">	}</span><br><span class="line">	Summer::<span class="built_in">mrt</span>(u);</span><br><span class="line">	Summer::<span class="built_in">access</span>(v);</span><br><span class="line">	Summer::<span class="built_in">splay</span>(v);</span><br><span class="line">	ans=Summer::sumv[v];</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">getPoint</span><span class="params">(<span class="type">int</span> u,<span class="type">int</span> v)</span> </span>{</span><br><span class="line">	<span class="type">int</span> x=<span class="built_in">find</span>(u),y=<span class="built_in">find</span>(v);</span><br><span class="line">	<span class="keyword">if</span>(x!=y) {</span><br><span class="line">		ans=<span class="number">-1</span>;</span><br><span class="line">		<span class="keyword">return</span>;</span><br><span class="line">	}</span><br><span class="line">	Pockets::<span class="built_in">mrt</span>(u);</span><br><span class="line">	Pockets::<span class="built_in">access</span>(v);</span><br><span class="line">	Pockets::<span class="built_in">splay</span>(v);</span><br><span class="line">	ans=Pockets::sumv[v];</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">link</span><span class="params">(<span class="type">int</span> u,<span class="type">int</span> v)</span> </span>{</span><br><span class="line">	<span class="type">int</span> x=<span class="built_in">find</span>(u),y=<span class="built_in">find</span>(v);</span><br><span class="line">	<span class="keyword">if</span>(x==y) {</span><br><span class="line">		Summer::<span class="built_in">mrt</span>(u);</span><br><span class="line">		Summer::<span class="built_in">access</span>(v);</span><br><span class="line">		Summer::<span class="built_in">splay</span>(v);</span><br><span class="line">		Summer::<span class="built_in">NaCly_Fish_Orz</span>(v);</span><br><span class="line">		</span><br><span class="line">		<span class="built_in">getPoint</span>(u,v);</span><br><span class="line">		<span class="keyword">if</span>(ans&gt;<span class="number">2</span>) {</span><br><span class="line">			++SummerPockets;</span><br><span class="line">			Pockets::<span class="built_in">mrt</span>(u);</span><br><span class="line">			Pockets::<span class="built_in">access</span>(v);</span><br><span class="line">			Pockets::<span class="built_in">splay</span>(v);</span><br><span class="line">			Pockets::num=<span class="number">0</span>;</span><br><span class="line">			Pockets::<span class="built_in">print</span>(v);</span><br><span class="line">			<span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;Pockets::num;++i)</span><br><span class="line">				Pockets::<span class="built_in">cut</span>(Pockets::st[i],Pockets::st[i+<span class="number">1</span>]);</span><br><span class="line">			<span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=Pockets::num;++i)</span><br><span class="line">				Pockets::<span class="built_in">link</span>(Pockets::st[i],SummerPockets);</span><br><span class="line">		}</span><br><span class="line">	} <span class="keyword">else</span> {</span><br><span class="line">		++tot; fa[y]=x;</span><br><span class="line">		Summer::val[tot]=<span class="number">1</span>;</span><br><span class="line">		Summer::<span class="built_in">link</span>(u,tot);</span><br><span class="line">		Summer::<span class="built_in">link</span>(tot,v);</span><br><span class="line">		</span><br><span class="line">		Pockets::<span class="built_in">link</span>(u,v);</span><br><span class="line">	}</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span> </span>{</span><br><span class="line">	<span class="built_in">scanf</span>(<span class="string">"%d%d"</span>,&amp;n,&amp;q);</span><br><span class="line">	tot=SummerPockets=n;</span><br><span class="line">	<span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n;++i)</span><br><span class="line">		fa[i]=i,Pockets::val[i]=<span class="number">1</span>;</span><br><span class="line">	<span class="keyword">while</span>(q--) {</span><br><span class="line">		<span class="built_in">scanf</span>(<span class="string">"%d%d%d"</span>,&amp;opt,&amp;u,&amp;v);</span><br><span class="line">		u^=last,v^=last;</span><br><span class="line">		<span class="keyword">switch</span>(opt) {</span><br><span class="line">			<span class="keyword">case</span> <span class="number">1</span>: {</span><br><span class="line">				<span class="built_in">link</span>(u,v);</span><br><span class="line">				<span class="keyword">break</span>;</span><br><span class="line">			}</span><br><span class="line">			<span class="keyword">case</span> <span class="number">2</span>: {</span><br><span class="line">				<span class="built_in">getEdge</span>(u,v);</span><br><span class="line">				<span class="keyword">if</span>(ans!=<span class="number">-1</span>) last=ans;</span><br><span class="line">				<span class="built_in">printf</span>(<span class="string">"%d\n"</span>,ans);</span><br><span class="line">				<span class="keyword">break</span>;</span><br><span class="line">			}</span><br><span class="line">			<span class="keyword">default</span>: {</span><br><span class="line">				<span class="built_in">getPoint</span>(u,v);</span><br><span class="line">				<span class="keyword">if</span>(ans!=<span class="number">-1</span>) last=ans;</span><br><span class="line">				<span class="built_in">printf</span>(<span class="string">"%d\n"</span>,ans);</span><br><span class="line">				<span class="keyword">break</span>;</span><br><span class="line">			}</span><br><span class="line">		}</span><br><span class="line">	}</span><br><span class="line">	<span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br><span class="line"> </span><br></pre></td></tr></tbody></table></figure>

<hr>
<h2 id="LCT-LCA"><a href="#LCT-LCA" class="headerlink" title="LCT+LCA"></a>LCT+LCA</h2><p><img src="https://img-blog.csdnimg.cn/3faf3b25eaf2445ba680c5d3876a14cd.png" alt="在这里插入图片描述"></p>
<p>1操作很容易联想到LCT的access，考虑对于剩下俩操作的维护，但其实对于树上点到根的路径权值具有可减性，于是维护这样一个距离，然后用树上差分回答2询问，因为一个点的子树在dfs序上是连续的一段，可以用线段树维护最大值回答3询问</p>
<p>这个题就成了3个板子的嵌套+巧妙的LCT，线段树和lca都是基础了不必再赘述</p>
<p>巧妙的LCT在于可以用这个题加深对access的理解，单独拿出access来说</p>
<figure class="highlight cpp"><table><tbody><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="type">void</span> <span class="title">access</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">    <span class="keyword">for</span> (<span class="type">int</span> y = <span class="number">0</span>; x; y = x, x = fa[x]) {</span><br><span class="line">        <span class="built_in">splay</span>(x); rs = y; <span class="comment">//pushup(x);</span></span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">access</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">    <span class="type">int</span> c;</span><br><span class="line">    <span class="keyword">for</span> (<span class="type">int</span> y = <span class="number">0</span>; x; y = x, x = fa[x]) {</span><br><span class="line">        <span class="built_in">splay</span>(x);</span><br><span class="line">        <span class="keyword">if</span> (rs) c = <span class="built_in">findrt</span>(rs), SEG::<span class="built_in">change</span>(<span class="number">1</span>, <span class="number">1</span>, n, dfn[c], dfn[c] + siz[c] - <span class="number">1</span>, <span class="number">1</span>);</span><br><span class="line">        <span class="keyword">if</span> (rs = y) c = <span class="built_in">findrt</span>(y), SEG::<span class="built_in">change</span>(<span class="number">1</span>, <span class="number">1</span>, n, dfn[c], dfn[c] + siz[c] - <span class="number">1</span>, <span class="number">-1</span>);</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table></figure>

<p>access实质是我们要对于x到根路径全部变成实边，我们要的是对于维护的信息进行修改</p>
<p>考虑性质，虚边有贡献，而实边没有贡献，在具体实现过程中，对于点x，遇到它的父亲到它为虚边则变实，然后整个子树到根节点的距离-1，然后把x的父亲原来连的实边的那个子树贡献+1，即可解决1操作</p>
<figure class="highlight cpp"><table><tbody><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br><span class="line">114</span><br><span class="line">115</span><br><span class="line">116</span><br><span class="line">117</span><br><span class="line">118</span><br><span class="line">119</span><br><span class="line">120</span><br><span class="line">121</span><br><span class="line">122</span><br><span class="line">123</span><br><span class="line">124</span><br><span class="line">125</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;iostream&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;cstdio&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;cmath&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;cstring&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;algorithm&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;queue&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">define</span> q(x, y) SEG::query(1, 1, n, x, y)</span></span><br><span class="line"><span class="meta">#<span class="keyword">define</span> inf 1e9</span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">file</span><span class="params">()</span> </span>{</span><br><span class="line">    <span class="built_in">freopen</span>(<span class="string">"read.in"</span>, <span class="string">"r"</span>, stdin);</span><br><span class="line">    <span class="built_in">freopen</span>(<span class="string">"write.out"</span>, <span class="string">"w"</span>, stdout);</span><br><span class="line">}</span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N = <span class="number">1e6</span> + <span class="number">10</span>;</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="type">int</span> <span class="title">read</span><span class="params">()</span> </span>{</span><br><span class="line">    <span class="type">int</span> sym = <span class="number">0</span>, res = <span class="number">0</span>; <span class="type">char</span> ch = <span class="built_in">getchar</span>();</span><br><span class="line">    <span class="keyword">while</span> (!<span class="built_in">isdigit</span>(ch)) sym |= (ch == <span class="string">'-'</span>), ch = <span class="built_in">getchar</span>();</span><br><span class="line">    <span class="keyword">while</span> (<span class="built_in">isdigit</span>(ch)) res = (res &lt;&lt; <span class="number">3</span>) + (res &lt;&lt; <span class="number">1</span>) + (ch ^ <span class="number">48</span>), ch = <span class="built_in">getchar</span>();</span><br><span class="line">    <span class="keyword">return</span> sym ? -res : res;</span><br><span class="line">}</span><br><span class="line"><span class="keyword">struct</span> <span class="title class_">EDGE</span> {</span><br><span class="line">    <span class="type">int</span> u, v, nxt;</span><br><span class="line">} edge[N];</span><br><span class="line"><span class="type">int</span> n, m, head[N], cnt, dfn[N], siz[N], depth[N], rev[N];</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">add</span><span class="params">(<span class="type">int</span> u, <span class="type">int</span> v)</span> </span>{edge[++cnt] = (EDGE){u, v, head[u]}; head[u] = cnt;}</span><br><span class="line"><span class="keyword">namespace</span> SEG {</span><br><span class="line">    <span class="type">int</span> tmax[N], tag[N];</span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> ls x &lt;&lt; 1</span></span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> rs x &lt;&lt; 1 | 1</span></span><br><span class="line">    <span class="function"><span class="type">void</span> <span class="title">pushup</span><span class="params">(<span class="type">int</span> x)</span> </span>{tmax[x] = <span class="built_in">max</span>(tmax[ls], tmax[rs]);}</span><br><span class="line">    <span class="function"><span class="type">void</span> <span class="title">update</span><span class="params">(<span class="type">int</span> x, <span class="type">int</span> t)</span> </span>{tmax[x] += t; tag[x] += t;}</span><br><span class="line">    <span class="function"><span class="type">void</span> <span class="title">pushdown</span><span class="params">(<span class="type">int</span> x, <span class="type">int</span> l, <span class="type">int</span> r, <span class="type">int</span> mid)</span> </span>{</span><br><span class="line">        <span class="keyword">if</span> (tag[x]) {</span><br><span class="line">            <span class="built_in">update</span>(ls, tag[x]); <span class="built_in">update</span>(rs, tag[x]); tag[x] = <span class="number">0</span>;</span><br><span class="line">        }</span><br><span class="line">    }</span><br><span class="line">    <span class="function"><span class="type">void</span> <span class="title">build</span><span class="params">(<span class="type">int</span> x, <span class="type">int</span> l, <span class="type">int</span> r)</span> </span>{</span><br><span class="line">        <span class="keyword">if</span> (l == r) {tmax[x] = depth[rev[l]]; <span class="keyword">return</span>;}</span><br><span class="line">        <span class="type">int</span> mid = l + r &gt;&gt; <span class="number">1</span>;</span><br><span class="line">        <span class="built_in">build</span>(ls, l, mid); <span class="built_in">build</span>(rs, mid + <span class="number">1</span>, r);</span><br><span class="line">        <span class="built_in">pushup</span>(x);</span><br><span class="line">    }</span><br><span class="line">    <span class="function"><span class="type">void</span> <span class="title">change</span><span class="params">(<span class="type">int</span> x, <span class="type">int</span> l, <span class="type">int</span> r, <span class="type">int</span> ln, <span class="type">int</span> rn, <span class="type">int</span> t)</span> </span>{</span><br><span class="line">        <span class="keyword">if</span> (ln &lt;= l &amp;&amp; r &lt;= rn) {<span class="built_in">update</span>(x, t); <span class="keyword">return</span>;}</span><br><span class="line">        <span class="type">int</span> mid = l + r &gt;&gt; <span class="number">1</span>; <span class="built_in">pushdown</span>(x, l, r, mid);</span><br><span class="line">        <span class="keyword">if</span> (mid &gt;= ln) <span class="built_in">change</span>(ls, l, mid, ln, rn, t);</span><br><span class="line">        <span class="keyword">if</span> (mid + <span class="number">1</span> &lt;= rn) <span class="built_in">change</span>(rs, mid + <span class="number">1</span>, r, ln, rn, t);</span><br><span class="line">        <span class="built_in">pushup</span>(x);</span><br><span class="line">    }</span><br><span class="line">    <span class="function"><span class="type">int</span> <span class="title">query</span><span class="params">(<span class="type">int</span> x, <span class="type">int</span> l, <span class="type">int</span> r, <span class="type">int</span> ln, <span class="type">int</span> rn)</span> </span>{</span><br><span class="line">        <span class="keyword">if</span> (ln &lt;= l &amp;&amp; r &lt;= rn) <span class="keyword">return</span> tmax[x];</span><br><span class="line">        <span class="type">int</span> mid = l + r &gt;&gt; <span class="number">1</span>, res = <span class="number">0</span>; <span class="built_in">pushdown</span>(x, l, r, mid);</span><br><span class="line">        <span class="keyword">if</span> (mid &gt;= ln) res = <span class="built_in">max</span>(res, <span class="built_in">query</span>(ls, l, mid, ln, rn));</span><br><span class="line">        <span class="keyword">if</span> (mid + <span class="number">1</span> &lt;= rn) res = <span class="built_in">max</span>(res, <span class="built_in">query</span>(rs, mid + <span class="number">1</span>, r, ln, rn));</span><br><span class="line">        <span class="keyword">return</span> res;</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="keyword">namespace</span> LCT {</span><br><span class="line">    <span class="type">int</span> son[N][<span class="number">2</span>], fa[N];</span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> ls son[x][0]</span></span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> rs son[x][1]</span></span><br><span class="line">    <span class="function"><span class="type">bool</span> <span class="title">l_r</span><span class="params">(<span class="type">int</span> x)</span> </span>{<span class="keyword">return</span> x == son[fa[x]][<span class="number">1</span>];}</span><br><span class="line">    <span class="function"><span class="type">bool</span> <span class="title">isroot</span><span class="params">(<span class="type">int</span> x)</span> </span>{<span class="keyword">return</span> son[fa[x]][<span class="number">0</span>] != x &amp;&amp; son[fa[x]][<span class="number">1</span>] != x;}</span><br><span class="line">    <span class="function"><span class="type">int</span> <span class="title">findrt</span><span class="params">(<span class="type">int</span> x)</span> </span>{<span class="keyword">while</span> (ls) x = ls; <span class="keyword">return</span> x;}</span><br><span class="line">    <span class="function"><span class="type">void</span> <span class="title">rotate</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">        <span class="type">int</span> y = fa[x], z = fa[y], kind = <span class="built_in">l_r</span>(x);</span><br><span class="line">        <span class="keyword">if</span> (!<span class="built_in">isroot</span>(y)) son[z][<span class="built_in">l_r</span>(y)] = x;</span><br><span class="line">        son[y][kind] = son[x][kind ^ <span class="number">1</span>]; fa[son[x][kind ^ <span class="number">1</span>]] = y;</span><br><span class="line">        son[x][kind ^ <span class="number">1</span>] = y; fa[y] = x; fa[x] = z;</span><br><span class="line">    }</span><br><span class="line">    <span class="function"><span class="type">void</span> <span class="title">splay</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">        <span class="keyword">for</span> (<span class="type">int</span> y = fa[x]; !<span class="built_in">isroot</span>(x); y = fa[x]) {</span><br><span class="line">            <span class="keyword">if</span> (!<span class="built_in">isroot</span>(y)) <span class="built_in">rotate</span>(<span class="built_in">l_r</span>(x) == <span class="built_in">l_r</span>(y) ? y : x); <span class="built_in">rotate</span>(x);</span><br><span class="line">        }</span><br><span class="line">    }</span><br><span class="line">    <span class="function"><span class="type">void</span> <span class="title">access</span><span class="params">(<span class="type">int</span> x)</span> </span>{</span><br><span class="line">        <span class="type">int</span> c;</span><br><span class="line">        <span class="keyword">for</span> (<span class="type">int</span> y = <span class="number">0</span>; x; y = x, x = fa[x]) {</span><br><span class="line">            <span class="built_in">splay</span>(x);</span><br><span class="line">            <span class="keyword">if</span> (rs) c = <span class="built_in">findrt</span>(rs), SEG::<span class="built_in">change</span>(<span class="number">1</span>, <span class="number">1</span>, n, dfn[c], dfn[c] + siz[c] - <span class="number">1</span>, <span class="number">1</span>);</span><br><span class="line">            <span class="keyword">if</span> (rs = y) c = <span class="built_in">findrt</span>(y), SEG::<span class="built_in">change</span>(<span class="number">1</span>, <span class="number">1</span>, n, dfn[c], dfn[c] + siz[c] - <span class="number">1</span>, <span class="number">-1</span>);</span><br><span class="line">        }</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="keyword">namespace</span> LCA {</span><br><span class="line">    <span class="type">int</span> top[N], son[N], fa[N];</span><br><span class="line">    <span class="function"><span class="type">void</span> <span class="title">dfs1</span><span class="params">(<span class="type">int</span> u, <span class="type">int</span> last)</span> </span>{</span><br><span class="line">        depth[u] = depth[last] + <span class="number">1</span>; siz[u] = <span class="number">1</span>; fa[u] = last;</span><br><span class="line">        <span class="keyword">for</span> (<span class="type">int</span> e = head[u]; e; e = edge[e].nxt) {</span><br><span class="line">            <span class="type">int</span> v = edge[e].v; <span class="keyword">if</span> (v == last) <span class="keyword">continue</span>; <span class="built_in">dfs1</span>(v, u);</span><br><span class="line">            siz[u] += siz[v]; <span class="keyword">if</span> (siz[v] &gt; siz[son[u]]) son[u] = v;</span><br><span class="line">        }</span><br><span class="line">    }</span><br><span class="line">    <span class="function"><span class="type">void</span> <span class="title">dfs2</span><span class="params">(<span class="type">int</span> u, <span class="type">int</span> front)</span> </span>{</span><br><span class="line">        dfn[u] = ++cnt; rev[cnt] = u; top[u] = front; <span class="keyword">if</span> (son[u]) <span class="built_in">dfs2</span>(son[u], front);</span><br><span class="line">        <span class="keyword">for</span> (<span class="type">int</span> e = head[u]; e; e = edge[e].nxt) {</span><br><span class="line">            <span class="type">int</span> v = edge[e].v; <span class="keyword">if</span> (v == fa[u] || v == son[u]) <span class="keyword">continue</span>; <span class="built_in">dfs2</span>(v, v);</span><br><span class="line">        }</span><br><span class="line">    }</span><br><span class="line">    <span class="function"><span class="type">int</span> <span class="title">lca</span><span class="params">(<span class="type">int</span> x, <span class="type">int</span> y)</span> </span>{</span><br><span class="line">        <span class="keyword">while</span> (top[x] != top[y]) depth[top[x]] &lt; depth[top[y]] ? y = fa[top[y]] : x = fa[top[x]];</span><br><span class="line">        <span class="keyword">return</span> depth[x] &lt; depth[y] ? x : y;</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span> </span>{</span><br><span class="line">    n = <span class="built_in">read</span>(); m = <span class="built_in">read</span>();</span><br><span class="line">    <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">1</span>; i &lt; n; i++) {</span><br><span class="line">        <span class="type">int</span> u = <span class="built_in">read</span>(), v = <span class="built_in">read</span>(); <span class="built_in">add</span>(u, v); <span class="built_in">add</span>(v, u);</span><br><span class="line">    }</span><br><span class="line">    cnt = <span class="number">0</span>; LCA::<span class="built_in">dfs1</span>(<span class="number">1</span>, <span class="number">0</span>); LCA::<span class="built_in">dfs2</span>(<span class="number">1</span>, <span class="number">1</span>); cnt = <span class="number">0</span>; SEG::<span class="built_in">build</span>(<span class="number">1</span>, <span class="number">1</span>, n);</span><br><span class="line">    <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">1</span>; i &lt;= n; i++) LCT::fa[i] = LCA::fa[i];</span><br><span class="line">    <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">1</span>; i &lt;= m; i++) {</span><br><span class="line">        <span class="type">int</span> opt = <span class="built_in">read</span>(), x = <span class="built_in">read</span>();</span><br><span class="line">        <span class="keyword">if</span> (opt == <span class="number">1</span>) LCT::<span class="built_in">access</span>(x);</span><br><span class="line">        <span class="keyword">if</span> (opt == <span class="number">2</span>) {</span><br><span class="line">            <span class="type">int</span> y = <span class="built_in">read</span>(), lca = LCA::<span class="built_in">lca</span>(x, y);</span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">"%d\n"</span>, <span class="built_in">q</span>(dfn[x], dfn[x]) + <span class="built_in">q</span>(dfn[y], dfn[y]) - <span class="number">2</span> * <span class="built_in">q</span>(dfn[lca], dfn[lca]) + <span class="number">1</span>);</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">if</span> (opt == <span class="number">3</span>) {</span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">"%d\n"</span>, <span class="built_in">q</span>(dfn[x], dfn[x] + siz[x] - <span class="number">1</span>));</span><br><span class="line">        }</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br><span class="line"></span><br></pre></td></tr></tbody></table></figure>

<hr>
<h2 id="LCT懒标记"><a href="#LCT懒标记" class="headerlink" title="LCT懒标记"></a>LCT懒标记</h2><p><img src="https://img-blog.csdnimg.cn/14df1f4844f94ddcbf8fd17f18b8d822.png" alt="在这里插入图片描述"></p>
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class="line">122</span><br><span class="line">123</span><br><span class="line">124</span><br><span class="line">125</span><br><span class="line">126</span><br><span class="line">127</span><br><span class="line">128</span><br><span class="line">129</span><br><span class="line">130</span><br><span class="line">131</span><br><span class="line">132</span><br><span class="line">133</span><br><span class="line">134</span><br><span class="line">135</span><br><span class="line">136</span><br><span class="line">137</span><br><span class="line">138</span><br><span class="line">139</span><br><span class="line">140</span><br><span class="line">141</span><br><span class="line">142</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string">&lt;bits/stdc++.h&gt;</span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"><span class="meta">#<span class="keyword">define</span> int long long</span></span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N=<span class="number">1e5</span>+<span class="number">10</span>;</span><br><span class="line"><span class="type">const</span> <span class="type">int</span> mod=<span class="number">51061</span>;</span><br><span class="line"><span class="keyword">struct</span> <span class="title class_">node</span>{</span><br><span class="line">    <span class="type">int</span> s[<span class="number">2</span>],p,v;</span><br><span class="line">    <span class="type">int</span> sum,rev,mul,add,sz;</span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> ls tr[u].s[0]</span></span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> lx tr[x].s[0]</span></span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> rs tr[u].s[1]</span></span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> rx tr[x].s[1]</span></span><br><span class="line">}tr[N];</span><br><span class="line"><span class="type">int</span> n,m,op,x,y;</span><br><span class="line"><span class="function"><span class="type">bool</span> <span class="keyword">inline</span> <span class="title">isroot</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    <span class="keyword">return</span> tr[tr[u].p].s[<span class="number">0</span>]!=u&amp;&amp;tr[tr[u].p].s[<span class="number">1</span>]!=u;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">pushup</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    tr[u].sum=(tr[ls].sum+tr[u].v+tr[rs].sum)%mod;</span><br><span class="line">    tr[u].sz=tr[ls].sz+tr[rs].sz+<span class="number">1</span>;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">pushrev</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    <span class="built_in">swap</span>(ls,rs);</span><br><span class="line">    tr[u].rev^=<span class="number">1</span>;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">pushmul</span><span class="params">(<span class="type">int</span> u,<span class="type">int</span> v)</span></span>{</span><br><span class="line">    tr[u].sum=tr[u].sum*v%mod;</span><br><span class="line">    tr[u].v=tr[u].v*v%mod;</span><br><span class="line">    tr[u].add=tr[u].add*v%mod;</span><br><span class="line">    tr[u].mul=tr[u].mul*v%mod;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">pushadd</span><span class="params">(<span class="type">int</span> u,<span class="type">int</span> v)</span></span>{</span><br><span class="line">    tr[u].sum=(tr[u].sum+tr[u].sz*v)%mod;</span><br><span class="line">    tr[u].v=(tr[u].v+v)%mod;</span><br><span class="line">    tr[u].add=(tr[u].add+v)%mod;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">pushdown</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(tr[u].rev){</span><br><span class="line">        <span class="built_in">pushrev</span>(ls),<span class="built_in">pushrev</span>(rs);</span><br><span class="line">        tr[u].rev=<span class="number">0</span>;</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">if</span>(tr[u].mul!=<span class="number">1</span>){</span><br><span class="line">        <span class="built_in">pushmul</span>(ls,tr[u].mul),<span class="built_in">pushmul</span>(rs,tr[u].mul);</span><br><span class="line">        tr[u].mul=<span class="number">1</span>;</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">if</span>(tr[u].add!=<span class="number">0</span>){</span><br><span class="line">        <span class="built_in">pushadd</span>(ls,tr[u].add),<span class="built_in">pushadd</span>(rs,tr[u].add);</span><br><span class="line">        tr[u].add=<span class="number">0</span>;</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">rotate</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="type">int</span> y=tr[x].p,z=tr[y].p;</span><br><span class="line">    <span class="type">int</span> k=tr[y].s[<span class="number">1</span>]==x;</span><br><span class="line">    <span class="keyword">if</span>(!<span class="built_in">isroot</span>(y))tr[z].s[tr[z].s[<span class="number">1</span>]==y]=x;</span><br><span class="line">    tr[x].p=z;</span><br><span class="line">    tr[y].s[k]=tr[x].s[k^<span class="number">1</span>],tr[tr[x].s[k^<span class="number">1</span>]].p=y;</span><br><span class="line">    tr[x].s[k^<span class="number">1</span>]=y,tr[y].p=x;</span><br><span class="line">    <span class="built_in">pushup</span>(y),<span class="built_in">pushup</span>(x);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">splay</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="type">static</span> <span class="type">int</span> stk[N];</span><br><span class="line">    <span class="type">int</span> tt=<span class="number">0</span>,t=x;</span><br><span class="line">    stk[++tt]=t;</span><br><span class="line">    <span class="keyword">while</span>(!<span class="built_in">isroot</span>(t))stk[++tt]=t=tr[t].p;</span><br><span class="line">    <span class="keyword">while</span>(tt)<span class="built_in">pushdown</span>(stk[tt--]);</span><br><span class="line">    <span class="keyword">while</span>(!<span class="built_in">isroot</span>(x)){</span><br><span class="line">        <span class="type">int</span> y=tr[x].p,z=tr[y].p;</span><br><span class="line">        <span class="keyword">if</span>(!<span class="built_in">isroot</span>(y)){</span><br><span class="line">            <span class="keyword">if</span>( (tr[z].s[<span class="number">1</span>]==y)^(tr[y].s[<span class="number">1</span>]==x) )<span class="built_in">rotate</span>(x);</span><br><span class="line">            <span class="keyword">else</span> <span class="built_in">rotate</span>(y);</span><br><span class="line">        }<span class="built_in">rotate</span>(x);</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">access</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="type">int</span> z=x;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> y=<span class="number">0</span>;x;y=x,x=tr[x].p){</span><br><span class="line">        <span class="built_in">splay</span>(x);</span><br><span class="line">        rx=y;</span><br><span class="line">        <span class="built_in">pushup</span>(x);</span><br><span class="line">    }</span><br><span class="line">    <span class="built_in">splay</span>(z);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">makeroot</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="built_in">access</span>(x);</span><br><span class="line">    <span class="built_in">pushrev</span>(x);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="keyword">inline</span> <span class="title">findroot</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    <span class="built_in">access</span>(u);</span><br><span class="line">    <span class="keyword">while</span>(ls)<span class="built_in">pushdown</span>(u),u=ls;</span><br><span class="line">    <span class="built_in">splay</span>(u);</span><br><span class="line">    <span class="keyword">return</span> u;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">split</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="built_in">makeroot</span>(x);</span><br><span class="line">    <span class="built_in">access</span>(y);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">link</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="built_in">makeroot</span>(x);</span><br><span class="line">    <span class="keyword">if</span>(<span class="built_in">findroot</span>(y)!=x)tr[x].p=y;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="keyword">inline</span> <span class="title">cut</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="built_in">makeroot</span>(x);</span><br><span class="line">    <span class="keyword">if</span>(<span class="built_in">findroot</span>(y)==x&amp;&amp;rx==y&amp;&amp;!tr[y].s[<span class="number">0</span>]){</span><br><span class="line">        tr[y].p=rx=<span class="number">0</span>;</span><br><span class="line">        <span class="built_in">pushup</span>(x);</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">signed</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line">    ios::<span class="built_in">sync_with_stdio</span>(<span class="number">0</span>);</span><br><span class="line">    cin.<span class="built_in">tie</span>(<span class="number">0</span>);</span><br><span class="line">    cout.<span class="built_in">tie</span>(<span class="number">0</span>);</span><br><span class="line">    cin&gt;&gt;n&gt;&gt;m;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n;i++)tr[i].mul=tr[i].v=tr[i].sz=tr[i].sum=<span class="number">1</span>;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;n;i++){</span><br><span class="line">        cin&gt;&gt;x&gt;&gt;y;</span><br><span class="line">        <span class="built_in">link</span>(x,y);</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">while</span>(m--){</span><br><span class="line">        <span class="type">char</span> c;</span><br><span class="line">        <span class="type">int</span> v;</span><br><span class="line">        cin&gt;&gt;c;</span><br><span class="line">        <span class="keyword">if</span>(c==<span class="string">'+'</span>){</span><br><span class="line">            cin&gt;&gt;x&gt;&gt;y&gt;&gt;v;</span><br><span class="line">            <span class="built_in">split</span>(x,y);</span><br><span class="line">            <span class="built_in">pushadd</span>(y,v);</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">if</span>(c==<span class="string">'-'</span>){</span><br><span class="line">            cin&gt;&gt;x&gt;&gt;y;<span class="built_in">cut</span>(x,y);</span><br><span class="line">            cin&gt;&gt;x&gt;&gt;y;<span class="built_in">link</span>(x,y);</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">if</span>(c==<span class="string">'*'</span>){</span><br><span class="line">            cin&gt;&gt;x&gt;&gt;y&gt;&gt;v;</span><br><span class="line">            <span class="built_in">split</span>(x,y);</span><br><span class="line">            <span class="built_in">pushmul</span>(y,v);</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">if</span>(c==<span class="string">'/'</span>){</span><br><span class="line">            cin&gt;&gt;x&gt;&gt;y;</span><br><span class="line">            <span class="built_in">split</span>(x,y);</span><br><span class="line">            cout&lt;&lt;tr[y].sum&lt;&lt;<span class="string">'\n'</span>;</span><br><span class="line">        }</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table></figure>

<hr>
<h2 id="用动态树解决树链剖分问题"><a href="#用动态树解决树链剖分问题" class="headerlink" title="用动态树解决树链剖分问题"></a>用动态树解决树链剖分问题</h2><p><img src="https://img-blog.csdnimg.cn/a79a5e489d514cd4a35aef17af47b734.png" alt="在这里插入图片描述"></p>
<figure class="highlight cpp"><table><tbody><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span 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class="line">152</span><br><span class="line">153</span><br><span class="line">154</span><br><span class="line">155</span><br><span class="line">156</span><br><span class="line">157</span><br><span class="line">158</span><br><span class="line">159</span><br><span class="line">160</span><br><span class="line">161</span><br><span class="line">162</span><br><span class="line">163</span><br><span class="line">164</span><br><span class="line">165</span><br><span class="line">166</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string">&lt;bits/stdc++.h&gt;</span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N=<span class="number">1e6</span>+<span class="number">10</span>;</span><br><span class="line"><span class="meta">#<span class="keyword">define</span> int long long</span></span><br><span class="line"><span class="type">int</span> n,m,p[N],stk[N];</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">find</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(p[x]!=x)p[x]=<span class="built_in">find</span>(p[x]);</span><br><span class="line">    <span class="keyword">return</span> p[x];</span><br><span class="line">}</span><br><span class="line"><span class="keyword">struct</span> <span class="title class_">Edge</span>{</span><br><span class="line">    <span class="type">int</span> x,y,a,b;</span><br><span class="line">    <span class="type">bool</span> <span class="keyword">operator</span>&lt;(<span class="type">const</span> Edge&amp;t)<span class="type">const</span>{</span><br><span class="line">        <span class="keyword">return</span> a&lt;t.a;</span><br><span class="line">    }</span><br><span class="line">}e[N];</span><br><span class="line"><span class="keyword">struct</span> <span class="title class_">node</span>{</span><br><span class="line">    <span class="type">int</span> s[<span class="number">2</span>],p,v;</span><br><span class="line">    <span class="type">int</span> max,min,sum,rev,lazy;</span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> ls tr[u].s[0]</span></span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> rs tr[u].s[1]</span></span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> lx tr[x].s[0]</span></span><br><span class="line">    <span class="meta">#<span class="keyword">define</span> rx tr[x].s[1]</span></span><br><span class="line">}tr[N];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">pushup</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    tr[u].sum=tr[ls].sum+tr[u].v+tr[rs].sum;</span><br><span class="line">    <span class="keyword">if</span>(u&gt;n)tr[u].max=tr[u].min=tr[u].v;</span><br><span class="line">    <span class="keyword">else</span> tr[u].max=<span class="number">-1e9</span>,tr[u].min=<span class="number">1e9</span>;</span><br><span class="line">    <span class="keyword">if</span>(ls){</span><br><span class="line">        tr[u].max=<span class="built_in">max</span>(tr[u].max,tr[ls].max);</span><br><span class="line">        tr[u].min=<span class="built_in">min</span>(tr[u].min,tr[ls].min);</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">if</span>(rs){</span><br><span class="line">        tr[u].max=<span class="built_in">max</span>(tr[u].max,tr[rs].max);</span><br><span class="line">        tr[u].min=<span class="built_in">min</span>(tr[u].min,tr[rs].min);</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">pushrev</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    <span class="built_in">swap</span>(ls,rs);</span><br><span class="line">    tr[u].rev^=<span class="number">1</span>;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">pushlazy</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    tr[u].sum=-tr[u].sum;</span><br><span class="line">    tr[u].max=-tr[u].max;</span><br><span class="line">    tr[u].min=-tr[u].min;</span><br><span class="line">    tr[u].v=-tr[u].v;</span><br><span class="line">    <span class="built_in">swap</span>(tr[u].max,tr[u].min);</span><br><span class="line">    tr[u].lazy^=<span class="number">1</span>;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">pushdown</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    <span class="keyword">if</span>(tr[u].rev){</span><br><span class="line">        <span class="built_in">pushrev</span>(ls);</span><br><span class="line">        <span class="built_in">pushrev</span>(rs);</span><br><span class="line">        tr[u].rev=<span class="number">0</span>;</span><br><span class="line">    }</span><br><span class="line">    <span class="keyword">if</span>(tr[u].lazy){</span><br><span class="line">        <span class="built_in">pushlazy</span>(ls);</span><br><span class="line">        <span class="built_in">pushlazy</span>(rs);</span><br><span class="line">        tr[u].lazy=<span class="number">0</span>;</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">bool</span> <span class="title">isroot</span><span class="params">(<span class="type">int</span> u)</span></span>{</span><br><span class="line">    <span class="keyword">return</span> tr[tr[u].p].s[<span class="number">0</span>]!=u&amp;&amp;tr[tr[u].p].s[<span class="number">1</span>]!=u;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">rotate</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="type">int</span> y=tr[x].p,z=tr[y].p;</span><br><span class="line">    <span class="type">int</span> k=tr[y].s[<span class="number">1</span>]==x;</span><br><span class="line">    <span class="keyword">if</span>(!<span class="built_in">isroot</span>(y))tr[z].s[tr[z].s[<span class="number">1</span>]==y]=x;</span><br><span class="line">    tr[x].p=z;</span><br><span class="line">    tr[y].s[k]=tr[x].s[k^<span class="number">1</span>],tr[tr[x].s[k^<span class="number">1</span>]].p=y;</span><br><span class="line">    tr[x].s[k^<span class="number">1</span>]=y,tr[y].p=x;</span><br><span class="line">    <span class="built_in">pushup</span>(y),<span class="built_in">pushup</span>(x);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">splay</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="type">int</span> top=<span class="number">0</span>,r=x;</span><br><span class="line">    stk[++top]=r;</span><br><span class="line">    <span class="keyword">while</span>(!<span class="built_in">isroot</span>(r))stk[++top]=r=tr[r].p;</span><br><span class="line">    <span class="keyword">while</span>(top)<span class="built_in">pushdown</span>(stk[top--]);</span><br><span class="line">    <span class="keyword">while</span>(!<span class="built_in">isroot</span>(x)){</span><br><span class="line">        <span class="type">int</span> y=tr[x].p,z=tr[y].p;</span><br><span class="line">        <span class="keyword">if</span>(!<span class="built_in">isroot</span>(y)){</span><br><span class="line">            <span class="keyword">if</span>((tr[z].s[<span class="number">1</span>]==y)^(tr[y].s[<span class="number">1</span>]==x))<span class="built_in">rotate</span>(x);</span><br><span class="line">            <span class="keyword">else</span> <span class="built_in">rotate</span>(y);</span><br><span class="line">        }</span><br><span class="line">        <span class="built_in">rotate</span>(x);</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">access</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="type">int</span> z=x;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> y=<span class="number">0</span>;x;y=x,x=tr[y].p){</span><br><span class="line">        <span class="built_in">splay</span>(x);</span><br><span class="line">        tr[x].s[<span class="number">1</span>]=y,<span class="built_in">pushup</span>(x);</span><br><span class="line">    }</span><br><span class="line">    <span class="built_in">splay</span>(z);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">makeroot</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="built_in">access</span>(x);</span><br><span class="line">    <span class="built_in">pushrev</span>(x);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">findroot</span><span class="params">(<span class="type">int</span> x)</span></span>{</span><br><span class="line">    <span class="built_in">access</span>(x);</span><br><span class="line">    <span class="keyword">while</span>(lx)<span class="built_in">pushdown</span>(x),x=lx;</span><br><span class="line">    <span class="built_in">splay</span>(x);</span><br><span class="line">    <span class="keyword">return</span> x;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">split</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="built_in">makeroot</span>(x);</span><br><span class="line">    <span class="built_in">access</span>(y);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">link</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="built_in">makeroot</span>(x);</span><br><span class="line">    <span class="keyword">if</span>(<span class="built_in">findroot</span>(y)!=x)tr[x].p=y;</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">cut</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> y)</span></span>{</span><br><span class="line">    <span class="built_in">makeroot</span>(x);</span><br><span class="line">    <span class="keyword">if</span>(<span class="built_in">findroot</span>(y)==x&amp;&amp;rx==y&amp;&amp;!tr[y].s[<span class="number">0</span>]){</span><br><span class="line">        tr[y].p=rx=<span class="number">0</span>;</span><br><span class="line">        <span class="built_in">pushup</span>(x);</span><br><span class="line">    }</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">change</span><span class="params">(<span class="type">int</span> x,<span class="type">int</span> w)</span></span>{</span><br><span class="line">    <span class="built_in">splay</span>(x);</span><br><span class="line">    tr[x].v=w;</span><br><span class="line">    <span class="built_in">pushup</span>(x);</span><br><span class="line">}</span><br><span class="line"><span class="function"><span class="type">signed</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line">    ios::<span class="built_in">sync_with_stdio</span>(<span class="number">0</span>);cin.<span class="built_in">tie</span>(<span class="number">0</span>);cout.<span class="built_in">tie</span>(<span class="number">0</span>);</span><br><span class="line">    cin&gt;&gt;n;</span><br><span class="line">    <span class="comment">//for(int i=1;i&lt;=n;i++)tr[i].max=-1e9,tr[i].min=1e9;</span></span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;n;i++){</span><br><span class="line">        <span class="type">int</span> a,b,c;</span><br><span class="line">        cin&gt;&gt;a&gt;&gt;b&gt;&gt;c;</span><br><span class="line">        a++,b++;</span><br><span class="line">        tr[i+n].max=tr[i+n].min=tr[i+n].sum=tr[i+n].v=c;</span><br><span class="line">        <span class="built_in">link</span>(a,i+n),<span class="built_in">link</span>(i+n,b);</span><br><span class="line">    }</span><br><span class="line">    cin&gt;&gt;m;</span><br><span class="line">    <span class="keyword">while</span>(m--){</span><br><span class="line">        string op;</span><br><span class="line">        <span class="type">int</span> x,y;</span><br><span class="line">        cin&gt;&gt;op&gt;&gt;x&gt;&gt;y;</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="string">"C"</span>){<span class="built_in">change</span>(x+n,y);<span class="keyword">continue</span>;}</span><br><span class="line">        x++,y++;</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="string">"N"</span>){</span><br><span class="line">            <span class="built_in">split</span>(x,y);</span><br><span class="line">            tr[y].max=-tr[y].max;</span><br><span class="line">            tr[y].min=-tr[y].min;</span><br><span class="line">            <span class="built_in">swap</span>(tr[y].max,tr[y].min);</span><br><span class="line">            tr[y].sum=-tr[y].sum;</span><br><span class="line">            tr[y].v=-tr[y].v;</span><br><span class="line">            tr[y].lazy^=<span class="number">1</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="string">"SUM"</span>){</span><br><span class="line">            <span class="built_in">split</span>(x,y);</span><br><span class="line">            cout&lt;&lt;tr[y].sum&lt;&lt;<span class="string">'\n'</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="string">"MAX"</span>){</span><br><span class="line">            <span class="built_in">split</span>(x,y);</span><br><span class="line">            cout&lt;&lt;tr[y].max&lt;&lt;<span class="string">'\n'</span>;</span><br><span class="line">        }</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="string">"MIN"</span>){</span><br><span class="line">            <span class="built_in">split</span>(x,y);</span><br><span class="line">            cout&lt;&lt;tr[y].min&lt;&lt;<span class="string">'\n'</span>;</span><br><span class="line">        }</span><br><span class="line">    }</span><br><span class="line">}</span><br></pre></td></tr></tbody></table></figure>
                
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